code: def perspective_transform_lafs(
      trans_01: Tensor, lafs_1: Tensor
  ) -> Tensor:
      r"""Function that applies perspective transformations to a set of local affine frames (LAFs).
  
      Args:
          trans_01: tensor for perspective transformations of shape :math:`(B, 3, 3)`.
          lafs_1: tensor of lafs of shape :math:`(B, N, 2, 3)`.
  
      Returns:
          tensor of N-dimensional points of shape :math:`(B, N, 2, 3)`.
  
      Examples:
          >>> rng = torch.manual_seed(0)
          >>> lafs_1 = torch.rand(2, 4, 2, 3)  # BxNx2x3
          >>> lafs_1
          tensor([[[[0.4963, 0.7682, 0.0885],
                    [0.1320, 0.3074, 0.6341]],
          <BLANKLINE>
                   [[0.4901, 0.8964, 0.4556],
                    [0.6323, 0.3489, 0.4017]],
          <BLANKLINE>
                   [[0.0223, 0.1689, 0.2939],
                    [0.5185, 0.6977, 0.8000]],
          <BLANKLINE>
                   [[0.1610, 0.2823, 0.6816],
                    [0.9152, 0.3971, 0.8742]]],
          <BLANKLINE>
          <BLANKLINE>
                  [[[0.4194, 0.5529, 0.9527],
                    [0.0362, 0.1852, 0.3734]],
          <BLANKLINE>
                   [[0.3051, 0.9320, 0.1759],
                    [0.2698, 0.1507, 0.0317]],
          <BLANKLINE>
                   [[0.2081, 0.9298, 0.7231],
                    [0.7423, 0.5263, 0.2437]],
          <BLANKLINE>
                   [[0.5846, 0.0332, 0.1387],
                    [0.2422, 0.8155, 0.7932]]]])
          >>> trans_01 = torch.eye(3).repeat(2, 1, 1)  # Bx3x3
          >>> trans_01.shape
          torch.Size([2, 3, 3])
          >>> lafs_0 = perspective_transform_lafs(trans_01, lafs_1)  # BxNx2x3
      """
      KORNIA_CHECK_LAF(lafs_1)
      if not torch.is_tensor(trans_01):
          raise TypeError("Input type is not a Tensor")
  
      if not trans_01.device == lafs_1.device:
          raise TypeError("Tensor must be in the same device")
  
      if not trans_01.shape[0] == lafs_1.shape[0]:
          raise ValueError(
              "Input batch size must be the same for both tensors"
          )
  
      if (not (trans_01.shape[-1] == 3)) or (
          not (trans_01.shape[-2] == 3)
      ):
          raise ValueError("Transformation should be homography")
  
      bs, n, _, _ = lafs_1.size()
      # First, we convert LAF to points
      threepts_1 = laf_to_three_points(lafs_1)
      points_1 = threepts_1.permute(0, 1, 3, 2).reshape(bs, n * 3, 2)
  
      # First, transform the points
      points_0 = transform_points(trans_01, points_1)
  
      # Back to LAF format
      threepts_0 = points_0.view(bs, n, 3, 2).permute(0, 1, 3, 2)
      return laf_from_three_points(threepts_0)
  
imports: import math
  from typing import List, Optional, Tuple, Union
  import torch
  import torch.nn.functional
  from kornia.core import Tensor, concatenate, cos, sin, stack, tensor, zeros
  from kornia.core.check import KORNIA_CHECK_LAF, KORNIA_CHECK_SHAPE
  from kornia.geometry.conversions import angle_to_rotation_matrix, convert_points_from_homogeneous, rad2deg
  from kornia.geometry.linalg import transform_points
  from kornia.geometry.transform import pyrdown
label_desc: Use image node_id 20 for calling a global function with example usage: perspective_transform_lafs(trans_01, lafs_1) and returns: laf_from_three_points